11 hours in Dubai. What can I do?

I want to go shopping and a little sightseeing in Dubai during my 11-hour layover, 5am-4pm, from Hong Kong going to Zurich. I live on an island that caters to tourists, so I don't like to be around kitschy places, I would like to see LEGIT Dubai places. And, I'm Filipino-American, so I won't attract so much attention as a tourist... Is there a place I can go to "feel" Dubai for the short time I am there? A place I can shop for a gutra and a dishdasha? With an American passport, will I be able to exit the airport? And, most importantly, what form of travel is the most reliable to and from the airport? Oooo, what about lunch?! I want to eat the Arabic way.